Setting origin of empty "group" object
You cannot set the origin for empties. They're just little more than an origin and a world matrix.
For Blender 2.82 and later:
In the header of the 3D View there is a drop down labelled Options. Within you can choose that the transform shall only affect the Parents. Select the empty, press SHIFT+S and click Selection to Cursor to move it to the cursor's location. The location of the children will not be modified.

Note that the &quot;affect only&quot; option already exists since Blender 2.81, but the Snap transform didn't support it before commit 3ba5461af0c8b1273d3daf87d050c24a690273be.
For Blender prior to 2.82:
If you want to have the empty at the 3D cursor's location, you will have to position the empty there. It is necessary to remove the parent relationship first ALT+P and add it back afterwards CTRL+P if you don't want the parented objects to move with the empty. With the empty selected, press SHIFT+S and click Selection to Cursor to move it to the cursor's location.